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Internal wave shocks in continuously stratified flows with velocity shear. (English) Zbl 1291.76077

Summary: The eigenvalue problem for momentum-conserving internal jumps in a stratified shear flow is developed, and solutions for several classes of flows are considered. It is shown that the presence of velocity shear significantly enhances the parameter range within which energetically-permissible shock solutions exist, and that the maximum allowable amplitude is increased when the ambient state possesses a baroclinic shear. It is also shown that the presence of steep regions in the stratification allow a class of larger-amplitude solutions compared to the case with smooth density gradients.

MSC:

76B55 Internal waves for incompressible inviscid fluids
76L05 Shock waves and blast waves in fluid mechanics
76B70 Stratification effects in inviscid fluids
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[1] Baines, P. G., Topographic Effects in Stratified Flows (1995), Cambridge University Press: Cambridge University Press New York · Zbl 0840.76001
[2] Farmer, D.; Armi, L., Stratified flow over topography: models versus observations, Proceedings of Royal Society A, 457, 2827-2830 (2001) · Zbl 1097.86502
[3] Z. Borden, E. Meiburg, Internal bores: an improved model via a detailed analysis of the energy budget, preprint.; Z. Borden, E. Meiburg, Internal bores: an improved model via a detailed analysis of the energy budget, preprint. · Zbl 1248.76035
[4] Benjamin, T. B., Gravity currents and related phenomena, Journal of fluid mechanics, 31, 209-248 (1968) · Zbl 0169.28503
[5] Su, C., Hydraulic jumps in an incompressible stratified fluid, Journal of fluid mechanics, 73, 33-47 (1976) · Zbl 0321.76046
[6] Long, R. R., Some aspects of the flows of stratified fluids. (i). a theoretical investigation, Tellus, 5, 42-58 (1953)
[7] Stanton, T. P.; Ostrovsky, L. A., Observations of highly nonlinear internal solitons over the continental shelf, Geophysical Research Letters, 25, 2695-2698 (1998)
[8] Benjamin, T. B., Internal waves of finite amplitude and permanent form, Journal of Fluid Mechanics, 25, 241-270 (1966) · Zbl 0145.23602
[9] Amick, C.; Turner, R., A global theory of internal waves in two-fluid systems, Transactions of the American Mathematical Society, 298, 431-481 (1986) · Zbl 0631.35029
[10] Sakai, T.; Redekopp, L. G., Models for strongly-nonlinear evolution of long internal waves in a two-layer stratification, Nonlinear Processes in Geophysics, 31-47 (2007)
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